Legendre transforms and Apéry's sequences
- 1 June 1995
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
- Vol. 58 (3), 358-375
- https://doi.org/10.1017/s1446788700038350
Abstract
This article studies particular sequences satisfying polynomial recurrences, among those Apéry's sequence which is shown to be the Legendre transform of the sequence . This results in the construction of simultaneous approximations of π 2/8 and ζ(3).Keywords
This publication has 7 references indexed in Scilit:
- Binomial identities — combinatorial and algorithmic aspectsDiscrete Mathematics, 1994
- Generalized q-Legendre polynomialsJournal of Computational and Applied Mathematics, 1993
- Recurrences for sums of powers of binomial coefficientsJournal of Combinatorial Theory, Series A, 1989
- Some recurrences for sums of powers of binomial coefficientsJournal of Number Theory, 1987
- A recurrence relation generalizing those of ApéryJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1984
- A proof that Euler missed ...The Mathematical Intelligencer, 1979
- Topics in Analytic Number TheoryPublished by Springer Science and Business Media LLC ,1973